Housing
What size is your tank? 10 gallons
What temperature is your tank? 79°
Does your tank have a filter? Yes (Whisper 10)
Does your tank have an air stone or other type of aeration? No
Is your tank heated? Yes
What tank mates does your betta fish live with? None

Food
What type of food do you feed your betta fish? Bio Gold betta pellets
How often do you feed your betta fish? I feed him 3 pellets in the morning and evening and fast him once a week

Maintenance*
How often do you perform a water change? Weekly
What percentage of the water do you change when you perform a water change? 50-75%
What type of additives do you add to the water when you perform a water change? I use API tap water cobditioner that claims it removes chlorine, chloramine, and heavy metals

Water Parameters:
Have you tested your water? If so, what are the following parameters?
Ammonia:
Nitrite:
Nitrate:
pH:
Hardness:
Alkalinity:*

Symptoms and Treatment
How has your betta fish's appearance changed? His tail looks tattered...I am thinking tail biting or possible fin rot but I am not seeing any black or red edging
How has your betta fish's behavior changed? He seems okay. He is eating like normal. He is swimming all over the tank...comes up for air here and there.
When did you start noticing the symptoms? I just noticed them tonight about an hour ago
Have you started treating your fish? No because I am not sure what's wrong yet
If so, how?
Does your fish have any history of being ill? No...not as far as I've had him
How old is your fish? I am not sure but I've only had him for a month.

Okay so hubby and I were gone Sunday night and all day today until about 8 p.m. When we left Splash was fine and looked normal and healthy. I fed him his evening meal and we turned off his tank light before we left. Tonight I get home and his behavior is still normal. He is swimming around and eating. Doesn't look lethargic.

However upon inspection I notice his tail fin looks sorta tattered. I know everything in his tank is smooth and not going to hurt him. So I am thinking either he is tail biting or possible fin rot? I don't see any black or red edging where his tail is tattered though. Just his usual blue and red. I don't know what it is. Please help me!

If he's tail biting what can I do to help him? I got plants and caves for him and I've never seen him bite before. Unless he was mad we left and got bored or lonely.

If it's fin rot (which I really pray it's not) what do I do? I don't know how this happened. I am trying to establish a cycle in my tank...did I do something wrong and cause this? I don't know how I can live with myself if I made him sick.

I am attaching two pics...the first one is his normal look. The second one is how his tail looks now...

HIs belly is gray. That's a sign of stress. Beyond that could literally be anything..

I don't see any biting.. I see some of the tips turning dark brown/black in the second photo? That's indicative of rot but in the photos doesn't look too bad at all..and he's a crowntail so his fins will be stringy like that..

I would switch pellets. Hikari used to be one of the best on the market now they are one of the worst because there is a lot of wheat in the pellet and it can lead to constipation and bloating. I like Omega One (you can feed up to six but watch to make sure he's pooping because you can also feed like 3-4) or NLS Betta which is my favorite. They're smaller and have some natural preventatives against internal infection. I feed 6-8 split up into two or three small meals.

While you are cycling, Prime can be helpful to you. It will render certain amount of ammonia in your tank harmless. This would be a conditioner instead of what you're using. Also stress coat at 1 ml per 1 gallon can help with biting I've found.. but I don't see signs of this from the photos you've shown.